Auto pistons at wemming chungs plant in shanghai are

Question

Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:

DAY	MEAN (MM)	RANGE (MM)
1	156.9	4.2
2	153.2	4.6
3	153.6	4.1
4	155.5	5.0
5	156.6	4.5

a) What is the value of x^_-?

b) What is the value of R^-?

c) What are the UCL_x^- and LCL^{_x^-}, using 3σ? Plot the data.

d) What are the UCL_R^- and LCL_R^-, using 3σ? Plot the data.

e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL_x^- and LCL_x^-?